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Existence for Nonlinear Evolution Equations and Application to Degenerate Parabolic Equation

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  • Ning Su
  • Li Zhang

Abstract

We consider an abstract Cauchy problem for a doubly nonlinear evolution equation of the form (d/dt)𝒜(u) + ℬ(u)∋f(t) in V′, t ∈ 0, T], where V is a real reflexive Banach space, 𝒜 and ℬ are maximal monotone operators (possibly multivalued) from V to its dual V′. In view of some practical applications, we assume that 𝒜 and ℬ are subdifferentials. By using the back difference approximation, existence is established, and our proof relies on the continuity of 𝒜 and the coerciveness of ℬ. As an application, we give the existence for a nonlinear degenerate parabolic equation.

Suggested Citation

  • Ning Su & Li Zhang, 2014. "Existence for Nonlinear Evolution Equations and Application to Degenerate Parabolic Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:567241
    DOI: 10.1155/2014/567241
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    References listed on IDEAS

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    1. Yakov Alber & Irina Ryazantseva, 2006. "Nonlinear Ill-posed Problems of Monotone Type," Springer Books, Springer, number 978-1-4020-4396-3, March.
    2. Regina S. Burachik & Alfredo N. Iusem, 2008. "Set-Valued Mappings and Enlargements of Monotone Operators," Springer Optimization and Its Applications, Springer, number 978-0-387-69757-4, January.
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